Properties

Label 1950.2.z.i.1849.2
Level $1950$
Weight $2$
Character 1950.1849
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.z (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1849.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.1849
Dual form 1950.2.z.i.1699.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(2.59808 + 1.50000i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{11} -1.00000i q^{12} +(2.59808 - 2.50000i) q^{13} +3.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} -1.00000i q^{18} +(-2.50000 + 4.33013i) q^{19} +3.00000 q^{21} +(-0.866025 - 0.500000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(2.59808 - 1.50000i) q^{28} +10.0000 q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.866025 - 0.500000i) q^{33} +(-0.500000 - 0.866025i) q^{36} +(-0.866025 + 0.500000i) q^{37} +5.00000i q^{38} +(1.00000 - 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.59808 - 1.50000i) q^{42} +(-1.73205 - 1.00000i) q^{43} -1.00000 q^{44} +(2.00000 - 3.46410i) q^{46} -9.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(1.00000 + 1.73205i) q^{49} +(-0.866025 - 3.50000i) q^{52} +13.0000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.50000 - 2.59808i) q^{56} +5.00000i q^{57} +(2.00000 - 3.46410i) q^{59} +(1.00000 - 1.73205i) q^{61} +(8.66025 - 5.00000i) q^{62} +(2.59808 - 1.50000i) q^{63} -1.00000 q^{64} -1.00000 q^{66} +(-10.3923 + 6.00000i) q^{67} +(2.00000 - 3.46410i) q^{69} +(1.00000 - 1.73205i) q^{71} +(-0.866025 - 0.500000i) q^{72} +16.0000i q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.50000 + 4.33013i) q^{76} -3.00000i q^{77} +(-0.866025 - 3.50000i) q^{78} +10.0000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-5.19615 - 3.00000i) q^{82} -12.0000i q^{83} +(1.50000 - 2.59808i) q^{84} -2.00000 q^{86} +(-0.866025 + 0.500000i) q^{88} +(0.500000 + 0.866025i) q^{89} +(10.5000 - 2.59808i) q^{91} -4.00000i q^{92} +(8.66025 - 5.00000i) q^{93} +(-4.50000 - 7.79423i) q^{94} -1.00000 q^{96} +(-10.3923 - 6.00000i) q^{97} +(1.73205 + 1.00000i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 2 q^{11} + 12 q^{14} - 2 q^{16} - 10 q^{19} + 12 q^{21} - 2 q^{24} + 4 q^{26} + 40 q^{31} - 2 q^{36} + 4 q^{39} - 12 q^{41} - 4 q^{44} + 8 q^{46} + 4 q^{49} - 2 q^{54} + 6 q^{56} + 8 q^{59} + 4 q^{61} - 4 q^{64} - 4 q^{66} + 8 q^{69} + 4 q^{71} - 2 q^{74} + 10 q^{76} + 40 q^{79} - 2 q^{81} + 6 q^{84} - 8 q^{86} + 2 q^{89} + 42 q^{91} - 18 q^{94} - 4 q^{96} - 4 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0.500000 0.866025i 0.204124 0.353553i
\(7\) 2.59808 + 1.50000i 0.981981 + 0.566947i 0.902867 0.429919i \(-0.141458\pi\)
0.0791130 + 0.996866i \(0.474791\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) 0 0
\(11\) −0.500000 0.866025i −0.150756 0.261116i 0.780750 0.624844i \(-0.214837\pi\)
−0.931505 + 0.363727i \(0.881504\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.59808 2.50000i 0.720577 0.693375i
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) 3.00000 0.654654
\(22\) −0.866025 0.500000i −0.184637 0.106600i
\(23\) 3.46410 2.00000i 0.722315 0.417029i −0.0932891 0.995639i \(-0.529738\pi\)
0.815604 + 0.578610i \(0.196405\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 0 0
\(26\) 1.00000 3.46410i 0.196116 0.679366i
\(27\) 1.00000i 0.192450i
\(28\) 2.59808 1.50000i 0.490990 0.283473i
\(29\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −0.866025 0.500000i −0.150756 0.0870388i
\(34\) 0 0
\(35\) 0 0
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) −0.866025 + 0.500000i −0.142374 + 0.0821995i −0.569495 0.821995i \(-0.692861\pi\)
0.427121 + 0.904194i \(0.359528\pi\)
\(38\) 5.00000i 0.811107i
\(39\) 1.00000 3.46410i 0.160128 0.554700i
\(40\) 0 0
\(41\) −3.00000 5.19615i −0.468521 0.811503i 0.530831 0.847477i \(-0.321880\pi\)
−0.999353 + 0.0359748i \(0.988546\pi\)
\(42\) 2.59808 1.50000i 0.400892 0.231455i
\(43\) −1.73205 1.00000i −0.264135 0.152499i 0.362084 0.932145i \(-0.382065\pi\)
−0.626219 + 0.779647i \(0.715399\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 2.00000 3.46410i 0.294884 0.510754i
\(47\) 9.00000i 1.31278i −0.754420 0.656392i \(-0.772082\pi\)
0.754420 0.656392i \(-0.227918\pi\)
\(48\) −0.866025 0.500000i −0.125000 0.0721688i
\(49\) 1.00000 + 1.73205i 0.142857 + 0.247436i
\(50\) 0 0
\(51\) 0 0
\(52\) −0.866025 3.50000i −0.120096 0.485363i
\(53\) 13.0000i 1.78569i 0.450367 + 0.892844i \(0.351293\pi\)
−0.450367 + 0.892844i \(0.648707\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 0 0
\(56\) 1.50000 2.59808i 0.200446 0.347183i
\(57\) 5.00000i 0.662266i
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) 8.66025 5.00000i 1.09985 0.635001i
\(63\) 2.59808 1.50000i 0.327327 0.188982i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) −10.3923 + 6.00000i −1.26962 + 0.733017i −0.974916 0.222571i \(-0.928555\pi\)
−0.294706 + 0.955588i \(0.595222\pi\)
\(68\) 0 0
\(69\) 2.00000 3.46410i 0.240772 0.417029i
\(70\) 0 0
\(71\) 1.00000 1.73205i 0.118678 0.205557i −0.800566 0.599245i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 16.0000i 1.87266i 0.351123 + 0.936329i \(0.385800\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 0 0
\(76\) 2.50000 + 4.33013i 0.286770 + 0.496700i
\(77\) 3.00000i 0.341882i
\(78\) −0.866025 3.50000i −0.0980581 0.396297i
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −5.19615 3.00000i −0.573819 0.331295i
\(83\) 12.0000i 1.31717i −0.752506 0.658586i \(-0.771155\pi\)
0.752506 0.658586i \(-0.228845\pi\)
\(84\) 1.50000 2.59808i 0.163663 0.283473i
\(85\) 0 0
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) −0.866025 + 0.500000i −0.0923186 + 0.0533002i
\(89\) 0.500000 + 0.866025i 0.0529999 + 0.0917985i 0.891308 0.453398i \(-0.149788\pi\)
−0.838308 + 0.545197i \(0.816455\pi\)
\(90\) 0 0
\(91\) 10.5000 2.59808i 1.10070 0.272352i
\(92\) 4.00000i 0.417029i
\(93\) 8.66025 5.00000i 0.898027 0.518476i
\(94\) −4.50000 7.79423i −0.464140 0.803913i
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) −10.3923 6.00000i −1.05518 0.609208i −0.131084 0.991371i \(-0.541846\pi\)
−0.924095 + 0.382164i \(0.875179\pi\)
\(98\) 1.73205 + 1.00000i 0.174964 + 0.101015i
\(99\) −1.00000 −0.100504
\(100\) 0 0
\(101\) −2.00000 3.46410i −0.199007 0.344691i 0.749199 0.662344i \(-0.230438\pi\)
−0.948207 + 0.317653i \(0.897105\pi\)
\(102\) 0 0
\(103\) 9.00000i 0.886796i 0.896325 + 0.443398i \(0.146227\pi\)
−0.896325 + 0.443398i \(0.853773\pi\)
\(104\) −2.50000 2.59808i −0.245145 0.254762i
\(105\) 0 0
\(106\) 6.50000 + 11.2583i 0.631336 + 1.09351i
\(107\) −5.19615 + 3.00000i −0.502331 + 0.290021i −0.729676 0.683793i \(-0.760329\pi\)
0.227345 + 0.973814i \(0.426996\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) −0.500000 + 0.866025i −0.0474579 + 0.0821995i
\(112\) 3.00000i 0.283473i
\(113\) 13.8564 + 8.00000i 1.30350 + 0.752577i 0.981003 0.193993i \(-0.0621440\pi\)
0.322498 + 0.946570i \(0.395477\pi\)
\(114\) 2.50000 + 4.33013i 0.234146 + 0.405554i
\(115\) 0 0
\(116\) 0 0
\(117\) −0.866025 3.50000i −0.0800641 0.323575i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 0 0
\(121\) 5.00000 8.66025i 0.454545 0.787296i
\(122\) 2.00000i 0.181071i
\(123\) −5.19615 3.00000i −0.468521 0.270501i
\(124\) 5.00000 8.66025i 0.449013 0.777714i
\(125\) 0 0
\(126\) 1.50000 2.59808i 0.133631 0.231455i
\(127\) 4.33013 2.50000i 0.384237 0.221839i −0.295423 0.955366i \(-0.595461\pi\)
0.679660 + 0.733527i \(0.262127\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −2.00000 −0.176090
\(130\) 0 0
\(131\) −15.0000 −1.31056 −0.655278 0.755388i \(-0.727449\pi\)
−0.655278 + 0.755388i \(0.727449\pi\)
\(132\) −0.866025 + 0.500000i −0.0753778 + 0.0435194i
\(133\) −12.9904 + 7.50000i −1.12641 + 0.650332i
\(134\) −6.00000 + 10.3923i −0.518321 + 0.897758i
\(135\) 0 0
\(136\) 0 0
\(137\) −13.8564 8.00000i −1.18383 0.683486i −0.226935 0.973910i \(-0.572870\pi\)
−0.956898 + 0.290424i \(0.906204\pi\)
\(138\) 4.00000i 0.340503i
\(139\) −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) 0 0
\(141\) −4.50000 7.79423i −0.378968 0.656392i
\(142\) 2.00000i 0.167836i
\(143\) −3.46410 1.00000i −0.289683 0.0836242i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 8.00000 + 13.8564i 0.662085 + 1.14676i
\(147\) 1.73205 + 1.00000i 0.142857 + 0.0824786i
\(148\) 1.00000i 0.0821995i
\(149\) −3.00000 + 5.19615i −0.245770 + 0.425685i −0.962348 0.271821i \(-0.912374\pi\)
0.716578 + 0.697507i \(0.245707\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) 4.33013 + 2.50000i 0.351220 + 0.202777i
\(153\) 0 0
\(154\) −1.50000 2.59808i −0.120873 0.209359i
\(155\) 0 0
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) 1.00000i 0.0798087i 0.999204 + 0.0399043i \(0.0127053\pi\)
−0.999204 + 0.0399043i \(0.987295\pi\)
\(158\) 8.66025 5.00000i 0.688973 0.397779i
\(159\) 6.50000 + 11.2583i 0.515484 + 0.892844i
\(160\) 0 0
\(161\) 12.0000 0.945732
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −17.3205 10.0000i −1.35665 0.783260i −0.367477 0.930033i \(-0.619778\pi\)
−0.989170 + 0.146772i \(0.953112\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −6.00000 10.3923i −0.465690 0.806599i
\(167\) −11.2583 + 6.50000i −0.871196 + 0.502985i −0.867745 0.497009i \(-0.834432\pi\)
−0.00345033 + 0.999994i \(0.501098\pi\)
\(168\) 3.00000i 0.231455i
\(169\) 0.500000 12.9904i 0.0384615 0.999260i
\(170\) 0 0
\(171\) 2.50000 + 4.33013i 0.191180 + 0.331133i
\(172\) −1.73205 + 1.00000i −0.132068 + 0.0762493i
\(173\) −7.79423 4.50000i −0.592584 0.342129i 0.173534 0.984828i \(-0.444481\pi\)
−0.766119 + 0.642699i \(0.777815\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.500000 + 0.866025i −0.0376889 + 0.0652791i
\(177\) 4.00000i 0.300658i
\(178\) 0.866025 + 0.500000i 0.0649113 + 0.0374766i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 6.00000 0.445976 0.222988 0.974821i \(-0.428419\pi\)
0.222988 + 0.974821i \(0.428419\pi\)
\(182\) 7.79423 7.50000i 0.577747 0.555937i
\(183\) 2.00000i 0.147844i
\(184\) −2.00000 3.46410i −0.147442 0.255377i
\(185\) 0 0
\(186\) 5.00000 8.66025i 0.366618 0.635001i
\(187\) 0 0
\(188\) −7.79423 4.50000i −0.568453 0.328196i
\(189\) 1.50000 2.59808i 0.109109 0.188982i
\(190\) 0 0
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) −13.8564 + 8.00000i −0.997406 + 0.575853i −0.907480 0.420096i \(-0.861996\pi\)
−0.0899262 + 0.995948i \(0.528663\pi\)
\(194\) −12.0000 −0.861550
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) −12.9904 + 7.50000i −0.925526 + 0.534353i −0.885394 0.464841i \(-0.846111\pi\)
−0.0401324 + 0.999194i \(0.512778\pi\)
\(198\) −0.866025 + 0.500000i −0.0615457 + 0.0355335i
\(199\) −1.00000 + 1.73205i −0.0708881 + 0.122782i −0.899291 0.437351i \(-0.855917\pi\)
0.828403 + 0.560133i \(0.189250\pi\)
\(200\) 0 0
\(201\) −6.00000 + 10.3923i −0.423207 + 0.733017i
\(202\) −3.46410 2.00000i −0.243733 0.140720i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 4.50000 + 7.79423i 0.313530 + 0.543050i
\(207\) 4.00000i 0.278019i
\(208\) −3.46410 1.00000i −0.240192 0.0693375i
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) 7.50000 + 12.9904i 0.516321 + 0.894295i 0.999820 + 0.0189499i \(0.00603229\pi\)
−0.483499 + 0.875345i \(0.660634\pi\)
\(212\) 11.2583 + 6.50000i 0.773225 + 0.446422i
\(213\) 2.00000i 0.137038i
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) 0 0
\(216\) −1.00000 −0.0680414
\(217\) 25.9808 + 15.0000i 1.76369 + 1.01827i
\(218\) 8.66025 5.00000i 0.586546 0.338643i
\(219\) 8.00000 + 13.8564i 0.540590 + 0.936329i
\(220\) 0 0
\(221\) 0 0
\(222\) 1.00000i 0.0671156i
\(223\) −9.52628 + 5.50000i −0.637927 + 0.368307i −0.783815 0.620994i \(-0.786729\pi\)
0.145889 + 0.989301i \(0.453396\pi\)
\(224\) −1.50000 2.59808i −0.100223 0.173591i
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) 17.3205 + 10.0000i 1.14960 + 0.663723i 0.948790 0.315906i \(-0.102309\pi\)
0.200812 + 0.979630i \(0.435642\pi\)
\(228\) 4.33013 + 2.50000i 0.286770 + 0.165567i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) 0 0
\(231\) −1.50000 2.59808i −0.0986928 0.170941i
\(232\) 0 0
\(233\) 10.0000i 0.655122i −0.944830 0.327561i \(-0.893773\pi\)
0.944830 0.327561i \(-0.106227\pi\)
\(234\) −2.50000 2.59808i −0.163430 0.169842i
\(235\) 0 0
\(236\) −2.00000 3.46410i −0.130189 0.225494i
\(237\) 8.66025 5.00000i 0.562544 0.324785i
\(238\) 0 0
\(239\) 2.00000 0.129369 0.0646846 0.997906i \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) −7.50000 + 12.9904i −0.483117 + 0.836784i −0.999812 0.0193858i \(-0.993829\pi\)
0.516695 + 0.856170i \(0.327162\pi\)
\(242\) 10.0000i 0.642824i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −1.00000 1.73205i −0.0640184 0.110883i
\(245\) 0 0
\(246\) −6.00000 −0.382546
\(247\) 4.33013 + 17.5000i 0.275519 + 1.11350i
\(248\) 10.0000i 0.635001i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) −5.50000 + 9.52628i −0.347157 + 0.601293i −0.985743 0.168257i \(-0.946186\pi\)
0.638586 + 0.769550i \(0.279520\pi\)
\(252\) 3.00000i 0.188982i
\(253\) −3.46410 2.00000i −0.217786 0.125739i
\(254\) 2.50000 4.33013i 0.156864 0.271696i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −20.7846 + 12.0000i −1.29651 + 0.748539i −0.979799 0.199983i \(-0.935911\pi\)
−0.316709 + 0.948523i \(0.602578\pi\)
\(258\) −1.73205 + 1.00000i −0.107833 + 0.0622573i
\(259\) −3.00000 −0.186411
\(260\) 0 0
\(261\) 0 0
\(262\) −12.9904 + 7.50000i −0.802548 + 0.463352i
\(263\) −2.59808 + 1.50000i −0.160204 + 0.0924940i −0.577959 0.816066i \(-0.696151\pi\)
0.417755 + 0.908560i \(0.362817\pi\)
\(264\) −0.500000 + 0.866025i −0.0307729 + 0.0533002i
\(265\) 0 0
\(266\) −7.50000 + 12.9904i −0.459855 + 0.796491i
\(267\) 0.866025 + 0.500000i 0.0529999 + 0.0305995i
\(268\) 12.0000i 0.733017i
\(269\) −10.0000 + 17.3205i −0.609711 + 1.05605i 0.381577 + 0.924337i \(0.375381\pi\)
−0.991288 + 0.131713i \(0.957952\pi\)
\(270\) 0 0
\(271\) 12.0000 + 20.7846i 0.728948 + 1.26258i 0.957328 + 0.289003i \(0.0933238\pi\)
−0.228380 + 0.973572i \(0.573343\pi\)
\(272\) 0 0
\(273\) 7.79423 7.50000i 0.471728 0.453921i
\(274\) −16.0000 −0.966595
\(275\) 0 0
\(276\) −2.00000 3.46410i −0.120386 0.208514i
\(277\) −19.9186 11.5000i −1.19679 0.690968i −0.236953 0.971521i \(-0.576149\pi\)
−0.959839 + 0.280553i \(0.909482\pi\)
\(278\) 9.00000i 0.539784i
\(279\) 5.00000 8.66025i 0.299342 0.518476i
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) −7.79423 4.50000i −0.464140 0.267971i
\(283\) −1.73205 + 1.00000i −0.102960 + 0.0594438i −0.550596 0.834772i \(-0.685599\pi\)
0.447636 + 0.894216i \(0.352266\pi\)
\(284\) −1.00000 1.73205i −0.0593391 0.102778i
\(285\) 0 0
\(286\) −3.50000 + 0.866025i −0.206959 + 0.0512092i
\(287\) 18.0000i 1.06251i
\(288\) −0.866025 + 0.500000i −0.0510310 + 0.0294628i
\(289\) −8.50000 14.7224i −0.500000 0.866025i
\(290\) 0 0
\(291\) −12.0000 −0.703452
\(292\) 13.8564 + 8.00000i 0.810885 + 0.468165i
\(293\) 11.2583 + 6.50000i 0.657719 + 0.379734i 0.791407 0.611289i \(-0.209349\pi\)
−0.133689 + 0.991023i \(0.542682\pi\)
\(294\) 2.00000 0.116642
\(295\) 0 0
\(296\) 0.500000 + 0.866025i 0.0290619 + 0.0503367i
\(297\) −0.866025 + 0.500000i −0.0502519 + 0.0290129i
\(298\) 6.00000i 0.347571i
\(299\) 4.00000 13.8564i 0.231326 0.801337i
\(300\) 0 0
\(301\) −3.00000 5.19615i −0.172917 0.299501i
\(302\) −5.19615 + 3.00000i −0.299005 + 0.172631i
\(303\) −3.46410 2.00000i −0.199007 0.114897i
\(304\) 5.00000 0.286770
\(305\) 0 0
\(306\) 0 0
\(307\) 18.0000i 1.02731i 0.857996 + 0.513657i \(0.171710\pi\)
−0.857996 + 0.513657i \(0.828290\pi\)
\(308\) −2.59808 1.50000i −0.148039 0.0854704i
\(309\) 4.50000 + 7.79423i 0.255996 + 0.443398i
\(310\) 0 0
\(311\) −12.0000 −0.680458 −0.340229 0.940343i \(-0.610505\pi\)
−0.340229 + 0.940343i \(0.610505\pi\)
\(312\) −3.46410 1.00000i −0.196116 0.0566139i
\(313\) 34.0000i 1.92179i 0.276907 + 0.960897i \(0.410691\pi\)
−0.276907 + 0.960897i \(0.589309\pi\)
\(314\) 0.500000 + 0.866025i 0.0282166 + 0.0488726i
\(315\) 0 0
\(316\) 5.00000 8.66025i 0.281272 0.487177i
\(317\) 19.0000i 1.06715i 0.845754 + 0.533573i \(0.179151\pi\)
−0.845754 + 0.533573i \(0.820849\pi\)
\(318\) 11.2583 + 6.50000i 0.631336 + 0.364502i
\(319\) 0 0
\(320\) 0 0
\(321\) −3.00000 + 5.19615i −0.167444 + 0.290021i
\(322\) 10.3923 6.00000i 0.579141 0.334367i
\(323\) 0 0
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −20.0000 −1.10770
\(327\) 8.66025 5.00000i 0.478913 0.276501i
\(328\) −5.19615 + 3.00000i −0.286910 + 0.165647i
\(329\) 13.5000 23.3827i 0.744279 1.28913i
\(330\) 0 0
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) −10.3923 6.00000i −0.570352 0.329293i
\(333\) 1.00000i 0.0547997i
\(334\) −6.50000 + 11.2583i −0.355664 + 0.616028i
\(335\) 0 0
\(336\) −1.50000 2.59808i −0.0818317 0.141737i
\(337\) 2.00000i 0.108947i 0.998515 + 0.0544735i \(0.0173480\pi\)
−0.998515 + 0.0544735i \(0.982652\pi\)
\(338\) −6.06218 11.5000i −0.329739 0.625518i
\(339\) 16.0000 0.869001
\(340\) 0 0
\(341\) −5.00000 8.66025i −0.270765 0.468979i
\(342\) 4.33013 + 2.50000i 0.234146 + 0.135185i
\(343\) 15.0000i 0.809924i
\(344\) −1.00000 + 1.73205i −0.0539164 + 0.0933859i
\(345\) 0 0
\(346\) −9.00000 −0.483843
\(347\) 24.2487 + 14.0000i 1.30174 + 0.751559i 0.980702 0.195507i \(-0.0626353\pi\)
0.321037 + 0.947067i \(0.395969\pi\)
\(348\) 0 0
\(349\) 18.0000 + 31.1769i 0.963518 + 1.66886i 0.713545 + 0.700609i \(0.247088\pi\)
0.249973 + 0.968253i \(0.419578\pi\)
\(350\) 0 0
\(351\) −2.50000 2.59808i −0.133440 0.138675i
\(352\) 1.00000i 0.0533002i
\(353\) 31.1769 18.0000i 1.65938 0.958043i 0.686378 0.727245i \(-0.259200\pi\)
0.973002 0.230799i \(-0.0741338\pi\)
\(354\) −2.00000 3.46410i −0.106299 0.184115i
\(355\) 0 0
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 10.3923 + 6.00000i 0.549250 + 0.317110i
\(359\) −34.0000 −1.79445 −0.897226 0.441572i \(-0.854421\pi\)
−0.897226 + 0.441572i \(0.854421\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 5.19615 3.00000i 0.273104 0.157676i
\(363\) 10.0000i 0.524864i
\(364\) 3.00000 10.3923i 0.157243 0.544705i
\(365\) 0 0
\(366\) −1.00000 1.73205i −0.0522708 0.0905357i
\(367\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(368\) −3.46410 2.00000i −0.180579 0.104257i
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −19.5000 + 33.7750i −1.01239 + 1.75351i
\(372\) 10.0000i 0.518476i
\(373\) 8.66025 + 5.00000i 0.448411 + 0.258890i 0.707159 0.707055i \(-0.249977\pi\)
−0.258748 + 0.965945i \(0.583310\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −9.00000 −0.464140
\(377\) 0 0
\(378\) 3.00000i 0.154303i
\(379\) −0.500000 0.866025i −0.0256833 0.0444847i 0.852898 0.522077i \(-0.174843\pi\)
−0.878581 + 0.477593i \(0.841509\pi\)
\(380\) 0 0
\(381\) 2.50000 4.33013i 0.128079 0.221839i
\(382\) 18.0000i 0.920960i
\(383\) −24.2487 14.0000i −1.23905 0.715367i −0.270151 0.962818i \(-0.587074\pi\)
−0.968900 + 0.247451i \(0.920407\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 0 0
\(386\) −8.00000 + 13.8564i −0.407189 + 0.705273i
\(387\) −1.73205 + 1.00000i −0.0880451 + 0.0508329i
\(388\) −10.3923 + 6.00000i −0.527589 + 0.304604i
\(389\) 16.0000 0.811232 0.405616 0.914044i \(-0.367057\pi\)
0.405616 + 0.914044i \(0.367057\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.73205 1.00000i 0.0874818 0.0505076i
\(393\) −12.9904 + 7.50000i −0.655278 + 0.378325i
\(394\) −7.50000 + 12.9904i −0.377845 + 0.654446i
\(395\) 0 0
\(396\) −0.500000 + 0.866025i −0.0251259 + 0.0435194i
\(397\) 28.5788 + 16.5000i 1.43433 + 0.828111i 0.997447 0.0714068i \(-0.0227489\pi\)
0.436884 + 0.899518i \(0.356082\pi\)
\(398\) 2.00000i 0.100251i
\(399\) −7.50000 + 12.9904i −0.375470 + 0.650332i
\(400\) 0 0
\(401\) −12.5000 21.6506i −0.624220 1.08118i −0.988691 0.149966i \(-0.952083\pi\)
0.364471 0.931215i \(-0.381250\pi\)
\(402\) 12.0000i 0.598506i
\(403\) 25.9808 25.0000i 1.29419 1.24534i
\(404\) −4.00000 −0.199007
\(405\) 0 0
\(406\) 0 0
\(407\) 0.866025 + 0.500000i 0.0429273 + 0.0247841i
\(408\) 0 0
\(409\) 8.50000 14.7224i 0.420298 0.727977i −0.575670 0.817682i \(-0.695259\pi\)
0.995968 + 0.0897044i \(0.0285922\pi\)
\(410\) 0 0
\(411\) −16.0000 −0.789222
\(412\) 7.79423 + 4.50000i 0.383994 + 0.221699i
\(413\) 10.3923 6.00000i 0.511372 0.295241i
\(414\) −2.00000 3.46410i −0.0982946 0.170251i
\(415\) 0 0
\(416\) −3.50000 + 0.866025i −0.171602 + 0.0424604i
\(417\) 9.00000i 0.440732i
\(418\) 4.33013 2.50000i 0.211793 0.122279i
\(419\) −14.0000 24.2487i −0.683945 1.18463i −0.973767 0.227547i \(-0.926930\pi\)
0.289822 0.957080i \(-0.406404\pi\)
\(420\) 0 0
\(421\) 20.0000 0.974740 0.487370 0.873195i \(-0.337956\pi\)
0.487370 + 0.873195i \(0.337956\pi\)
\(422\) 12.9904 + 7.50000i 0.632362 + 0.365094i
\(423\) −7.79423 4.50000i −0.378968 0.218797i
\(424\) 13.0000 0.631336
\(425\) 0 0
\(426\) −1.00000 1.73205i −0.0484502 0.0839181i
\(427\) 5.19615 3.00000i 0.251459 0.145180i
\(428\) 6.00000i 0.290021i
\(429\) −3.50000 + 0.866025i −0.168982 + 0.0418121i
\(430\) 0 0
\(431\) −18.0000 31.1769i −0.867029 1.50174i −0.865018 0.501741i \(-0.832693\pi\)
−0.00201168 0.999998i \(-0.500640\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 13.8564 + 8.00000i 0.665896 + 0.384455i 0.794520 0.607238i \(-0.207723\pi\)
−0.128624 + 0.991693i \(0.541056\pi\)
\(434\) 30.0000 1.44005
\(435\) 0 0
\(436\) 5.00000 8.66025i 0.239457 0.414751i
\(437\) 20.0000i 0.956730i
\(438\) 13.8564 + 8.00000i 0.662085 + 0.382255i
\(439\) −5.00000 8.66025i −0.238637 0.413331i 0.721686 0.692220i \(-0.243367\pi\)
−0.960323 + 0.278889i \(0.910034\pi\)
\(440\) 0 0
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 18.0000i 0.855206i 0.903967 + 0.427603i \(0.140642\pi\)
−0.903967 + 0.427603i \(0.859358\pi\)
\(444\) 0.500000 + 0.866025i 0.0237289 + 0.0410997i
\(445\) 0 0
\(446\) −5.50000 + 9.52628i −0.260433 + 0.451082i
\(447\) 6.00000i 0.283790i
\(448\) −2.59808 1.50000i −0.122748 0.0708683i
\(449\) −7.50000 + 12.9904i −0.353947 + 0.613054i −0.986937 0.161106i \(-0.948494\pi\)
0.632990 + 0.774160i \(0.281827\pi\)
\(450\) 0 0
\(451\) −3.00000 + 5.19615i −0.141264 + 0.244677i
\(452\) 13.8564 8.00000i 0.651751 0.376288i
\(453\) −5.19615 + 3.00000i −0.244137 + 0.140952i
\(454\) 20.0000 0.938647
\(455\) 0 0
\(456\) 5.00000 0.234146
\(457\) 19.0526 11.0000i 0.891241 0.514558i 0.0168929 0.999857i \(-0.494623\pi\)
0.874348 + 0.485299i \(0.161289\pi\)
\(458\) 8.66025 5.00000i 0.404667 0.233635i
\(459\) 0 0
\(460\) 0 0
\(461\) 6.00000 10.3923i 0.279448 0.484018i −0.691800 0.722089i \(-0.743182\pi\)
0.971248 + 0.238071i \(0.0765153\pi\)
\(462\) −2.59808 1.50000i −0.120873 0.0697863i
\(463\) 16.0000i 0.743583i 0.928316 + 0.371792i \(0.121256\pi\)
−0.928316 + 0.371792i \(0.878744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −5.00000 8.66025i −0.231621 0.401179i
\(467\) 36.0000i 1.66588i −0.553362 0.832941i \(-0.686655\pi\)
0.553362 0.832941i \(-0.313345\pi\)
\(468\) −3.46410 1.00000i −0.160128 0.0462250i
\(469\) −36.0000 −1.66233
\(470\) 0 0
\(471\) 0.500000 + 0.866025i 0.0230388 + 0.0399043i
\(472\) −3.46410 2.00000i −0.159448 0.0920575i
\(473\) 2.00000i 0.0919601i
\(474\) 5.00000 8.66025i 0.229658 0.397779i
\(475\) 0 0
\(476\) 0 0
\(477\) 11.2583 + 6.50000i 0.515484 + 0.297615i
\(478\) 1.73205 1.00000i 0.0792222 0.0457389i
\(479\) −4.00000 6.92820i −0.182765 0.316558i 0.760056 0.649857i \(-0.225171\pi\)
−0.942821 + 0.333300i \(0.891838\pi\)
\(480\) 0 0
\(481\) −1.00000 + 3.46410i −0.0455961 + 0.157949i
\(482\) 15.0000i 0.683231i
\(483\) 10.3923 6.00000i 0.472866 0.273009i
\(484\) −5.00000 8.66025i −0.227273 0.393648i
\(485\) 0 0
\(486\) −1.00000 −0.0453609
\(487\) −30.3109 17.5000i −1.37352 0.793001i −0.382148 0.924101i \(-0.624816\pi\)
−0.991369 + 0.131100i \(0.958149\pi\)
\(488\) −1.73205 1.00000i −0.0784063 0.0452679i
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −12.5000 21.6506i −0.564117 0.977079i −0.997131 0.0756923i \(-0.975883\pi\)
0.433014 0.901387i \(-0.357450\pi\)
\(492\) −5.19615 + 3.00000i −0.234261 + 0.135250i
\(493\) 0 0
\(494\) 12.5000 + 12.9904i 0.562402 + 0.584465i
\(495\) 0 0
\(496\) −5.00000 8.66025i −0.224507 0.388857i
\(497\) 5.19615 3.00000i 0.233079 0.134568i
\(498\) −10.3923 6.00000i −0.465690 0.268866i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) −6.50000 + 11.2583i −0.290399 + 0.502985i
\(502\) 11.0000i 0.490954i
\(503\) −0.866025 0.500000i −0.0386142 0.0222939i 0.480569 0.876957i \(-0.340430\pi\)
−0.519183 + 0.854663i \(0.673764\pi\)
\(504\) −1.50000 2.59808i −0.0668153 0.115728i
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) −6.06218 11.5000i −0.269231 0.510733i
\(508\) 5.00000i 0.221839i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) −24.0000 + 41.5692i −1.06170 + 1.83891i
\(512\) 1.00000i 0.0441942i
\(513\) 4.33013 + 2.50000i 0.191180 + 0.110378i
\(514\) −12.0000 + 20.7846i −0.529297 + 0.916770i
\(515\) 0 0
\(516\) −1.00000 + 1.73205i −0.0440225 + 0.0762493i
\(517\) −7.79423 + 4.50000i −0.342790 + 0.197910i
\(518\) −2.59808 + 1.50000i −0.114153 + 0.0659062i
\(519\) −9.00000 −0.395056
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 0 0
\(523\) −5.19615 + 3.00000i −0.227212 + 0.131181i −0.609285 0.792951i \(-0.708544\pi\)
0.382073 + 0.924132i \(0.375210\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) −1.50000 + 2.59808i −0.0654031 + 0.113282i
\(527\) 0 0
\(528\) 1.00000i 0.0435194i
\(529\) −3.50000 + 6.06218i −0.152174 + 0.263573i
\(530\) 0 0
\(531\) −2.00000 3.46410i −0.0867926 0.150329i
\(532\) 15.0000i 0.650332i
\(533\) −20.7846 6.00000i −0.900281 0.259889i
\(534\) 1.00000 0.0432742
\(535\) 0 0
\(536\) 6.00000 + 10.3923i 0.259161 + 0.448879i
\(537\) 10.3923 + 6.00000i 0.448461 + 0.258919i
\(538\) 20.0000i 0.862261i
\(539\) 1.00000 1.73205i 0.0430730 0.0746047i
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 20.7846 + 12.0000i 0.892775 + 0.515444i
\(543\) 5.19615 3.00000i 0.222988 0.128742i
\(544\) 0 0
\(545\) 0 0
\(546\) 3.00000 10.3923i 0.128388 0.444750i
\(547\) 34.0000i 1.45374i 0.686778 + 0.726868i \(0.259025\pi\)
−0.686778 + 0.726868i \(0.740975\pi\)
\(548\) −13.8564 + 8.00000i −0.591916 + 0.341743i
\(549\) −1.00000 1.73205i −0.0426790 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) −3.46410 2.00000i −0.147442 0.0851257i
\(553\) 25.9808 + 15.0000i 1.10481 + 0.637865i
\(554\) −23.0000 −0.977176
\(555\) 0 0
\(556\) 4.50000 + 7.79423i 0.190843 + 0.330549i
\(557\) −2.59808 + 1.50000i −0.110084 + 0.0635570i −0.554031 0.832496i \(-0.686911\pi\)
0.443947 + 0.896053i \(0.353578\pi\)
\(558\) 10.0000i 0.423334i
\(559\) −7.00000 + 1.73205i −0.296068 + 0.0732579i
\(560\) 0 0
\(561\) 0 0
\(562\) 8.66025 5.00000i 0.365311 0.210912i
\(563\) 20.7846 + 12.0000i 0.875967 + 0.505740i 0.869326 0.494238i \(-0.164553\pi\)
0.00664037 + 0.999978i \(0.497886\pi\)
\(564\) −9.00000 −0.378968
\(565\) 0 0
\(566\) −1.00000 + 1.73205i −0.0420331 + 0.0728035i
\(567\) 3.00000i 0.125988i
\(568\) −1.73205 1.00000i −0.0726752 0.0419591i
\(569\) −5.50000 9.52628i −0.230572 0.399362i 0.727405 0.686209i \(-0.240726\pi\)
−0.957977 + 0.286846i \(0.907393\pi\)
\(570\) 0 0
\(571\) 7.00000 0.292941 0.146470 0.989215i \(-0.453209\pi\)
0.146470 + 0.989215i \(0.453209\pi\)
\(572\) −2.59808 + 2.50000i −0.108631 + 0.104530i
\(573\) 18.0000i 0.751961i
\(574\) −9.00000 15.5885i −0.375653 0.650650i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 18.0000i 0.749350i 0.927156 + 0.374675i \(0.122246\pi\)
−0.927156 + 0.374675i \(0.877754\pi\)
\(578\) −14.7224 8.50000i −0.612372 0.353553i
\(579\) −8.00000 + 13.8564i −0.332469 + 0.575853i
\(580\) 0 0
\(581\) 18.0000 31.1769i 0.746766 1.29344i
\(582\) −10.3923 + 6.00000i −0.430775 + 0.248708i
\(583\) 11.2583 6.50000i 0.466272 0.269202i
\(584\) 16.0000 0.662085
\(585\) 0 0
\(586\) 13.0000 0.537025
\(587\) −15.5885 + 9.00000i −0.643404 + 0.371470i −0.785925 0.618322i \(-0.787813\pi\)
0.142520 + 0.989792i \(0.454479\pi\)
\(588\) 1.73205 1.00000i 0.0714286 0.0412393i
\(589\) −25.0000 + 43.3013i −1.03011 + 1.78420i
\(590\) 0 0
\(591\) −7.50000 + 12.9904i −0.308509 + 0.534353i
\(592\) 0.866025 + 0.500000i 0.0355934 + 0.0205499i
\(593\) 28.0000i 1.14982i −0.818216 0.574911i \(-0.805037\pi\)
0.818216 0.574911i \(-0.194963\pi\)
\(594\) −0.500000 + 0.866025i −0.0205152 + 0.0355335i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 2.00000i 0.0818546i
\(598\) −3.46410 14.0000i −0.141658 0.572503i
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) 13.5000 + 23.3827i 0.550676 + 0.953800i 0.998226 + 0.0595404i \(0.0189635\pi\)
−0.447549 + 0.894259i \(0.647703\pi\)
\(602\) −5.19615 3.00000i −0.211779 0.122271i
\(603\) 12.0000i 0.488678i
\(604\) −3.00000 + 5.19615i −0.122068 + 0.211428i
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) −32.0429 18.5000i −1.30058 0.750892i −0.320079 0.947391i \(-0.603709\pi\)
−0.980504 + 0.196499i \(0.937043\pi\)
\(608\) 4.33013 2.50000i 0.175610 0.101388i
\(609\) 0 0
\(610\) 0 0
\(611\) −22.5000 23.3827i −0.910253 0.945962i
\(612\) 0 0
\(613\) −19.9186 + 11.5000i −0.804504 + 0.464481i −0.845044 0.534697i \(-0.820426\pi\)
0.0405396 + 0.999178i \(0.487092\pi\)
\(614\) 9.00000 + 15.5885i 0.363210 + 0.629099i
\(615\) 0 0
\(616\) −3.00000 −0.120873
\(617\) 5.19615 + 3.00000i 0.209189 + 0.120775i 0.600935 0.799298i \(-0.294795\pi\)
−0.391745 + 0.920074i \(0.628129\pi\)
\(618\) 7.79423 + 4.50000i 0.313530 + 0.181017i
\(619\) 31.0000 1.24600 0.622998 0.782224i \(-0.285915\pi\)
0.622998 + 0.782224i \(0.285915\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) −10.3923 + 6.00000i −0.416693 + 0.240578i
\(623\) 3.00000i 0.120192i
\(624\) −3.50000 + 0.866025i −0.140112 + 0.0346688i
\(625\) 0 0
\(626\) 17.0000 + 29.4449i 0.679457 + 1.17685i
\(627\) 4.33013 2.50000i 0.172929 0.0998404i
\(628\) 0.866025 + 0.500000i 0.0345582 + 0.0199522i
\(629\) 0 0
\(630\) 0 0
\(631\) 2.00000 3.46410i 0.0796187 0.137904i −0.823467 0.567365i \(-0.807963\pi\)
0.903085 + 0.429461i \(0.141296\pi\)
\(632\) 10.0000i 0.397779i
\(633\) 12.9904 + 7.50000i 0.516321 + 0.298098i
\(634\) 9.50000 + 16.4545i 0.377293 + 0.653491i
\(635\) 0 0
\(636\) 13.0000 0.515484
\(637\) 6.92820 + 2.00000i 0.274505 + 0.0792429i
\(638\) 0 0
\(639\) −1.00000 1.73205i −0.0395594 0.0685189i
\(640\) 0 0
\(641\) 4.50000 7.79423i 0.177739 0.307854i −0.763367 0.645966i \(-0.776455\pi\)
0.941106 + 0.338112i \(0.109788\pi\)
\(642\) 6.00000i 0.236801i
\(643\) −38.1051 22.0000i −1.50272 0.867595i −0.999995 0.00314839i \(-0.998998\pi\)
−0.502724 0.864447i \(-0.667669\pi\)
\(644\) 6.00000 10.3923i 0.236433 0.409514i
\(645\) 0 0
\(646\) 0 0
\(647\) 7.79423 4.50000i 0.306423 0.176913i −0.338902 0.940822i \(-0.610055\pi\)
0.645325 + 0.763908i \(0.276722\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −4.00000 −0.157014
\(650\) 0 0
\(651\) 30.0000 1.17579
\(652\) −17.3205 + 10.0000i −0.678323 + 0.391630i
\(653\) −35.5070 + 20.5000i −1.38950 + 0.802227i −0.993259 0.115920i \(-0.963018\pi\)
−0.396239 + 0.918147i \(0.629685\pi\)
\(654\) 5.00000 8.66025i 0.195515 0.338643i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 13.8564 + 8.00000i 0.540590 + 0.312110i
\(658\) 27.0000i 1.05257i
\(659\) 2.00000 3.46410i 0.0779089 0.134942i −0.824439 0.565951i \(-0.808509\pi\)
0.902348 + 0.431009i \(0.141842\pi\)
\(660\) 0 0
\(661\) −7.00000 12.1244i −0.272268 0.471583i 0.697174 0.716902i \(-0.254441\pi\)
−0.969442 + 0.245319i \(0.921107\pi\)
\(662\) 28.0000i 1.08825i
\(663\) 0 0
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) 0.500000 + 0.866025i 0.0193746 + 0.0335578i
\(667\) 0 0
\(668\) 13.0000i 0.502985i
\(669\) −5.50000 + 9.52628i −0.212642 + 0.368307i
\(670\) 0 0
\(671\) −2.00000 −0.0772091
\(672\) −2.59808 1.50000i −0.100223 0.0578638i
\(673\) 27.7128 16.0000i 1.06825 0.616755i 0.140548 0.990074i \(-0.455114\pi\)
0.927703 + 0.373319i \(0.121780\pi\)
\(674\) 1.00000 + 1.73205i 0.0385186 + 0.0667161i
\(675\) 0 0
\(676\) −11.0000 6.92820i −0.423077 0.266469i
\(677\) 26.0000i 0.999261i −0.866239 0.499631i \(-0.833469\pi\)
0.866239 0.499631i \(-0.166531\pi\)
\(678\) 13.8564 8.00000i 0.532152 0.307238i
\(679\) −18.0000 31.1769i −0.690777 1.19646i
\(680\) 0 0
\(681\) 20.0000 0.766402
\(682\) −8.66025 5.00000i −0.331618 0.191460i
\(683\) −22.5167 13.0000i −0.861576 0.497431i 0.00296369 0.999996i \(-0.499057\pi\)
−0.864540 + 0.502564i \(0.832390\pi\)
\(684\) 5.00000 0.191180
\(685\) 0 0
\(686\) −7.50000 12.9904i −0.286351 0.495975i
\(687\) 8.66025 5.00000i 0.330409 0.190762i
\(688\) 2.00000i 0.0762493i
\(689\) 32.5000 + 33.7750i 1.23815 + 1.28672i
\(690\) 0 0
\(691\) −16.5000 28.5788i −0.627690 1.08719i −0.988014 0.154363i \(-0.950667\pi\)
0.360325 0.932827i \(-0.382666\pi\)
\(692\) −7.79423 + 4.50000i −0.296292 + 0.171064i
\(693\) −2.59808 1.50000i −0.0986928 0.0569803i
\(694\) 28.0000 1.06287
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 31.1769 + 18.0000i 1.18006 + 0.681310i
\(699\) −5.00000 8.66025i −0.189117 0.327561i
\(700\) 0 0
\(701\) 4.00000 0.151078 0.0755390 0.997143i \(-0.475932\pi\)
0.0755390 + 0.997143i \(0.475932\pi\)
\(702\) −3.46410 1.00000i −0.130744 0.0377426i
\(703\) 5.00000i 0.188579i
\(704\) 0.500000 + 0.866025i 0.0188445 + 0.0326396i
\(705\) 0 0
\(706\) 18.0000 31.1769i 0.677439 1.17336i
\(707\) 12.0000i 0.451306i
\(708\) −3.46410 2.00000i −0.130189 0.0751646i
\(709\) 2.00000 3.46410i 0.0751116 0.130097i −0.826023 0.563636i \(-0.809402\pi\)
0.901135 + 0.433539i \(0.142735\pi\)
\(710\) 0 0
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) 0.866025 0.500000i 0.0324557 0.0187383i
\(713\) 34.6410 20.0000i 1.29732 0.749006i
\(714\) 0 0
\(715\) 0 0
\(716\) 12.0000 0.448461
\(717\) 1.73205 1.00000i 0.0646846 0.0373457i
\(718\) −29.4449 + 17.0000i −1.09887 + 0.634434i
\(719\) 18.0000 31.1769i 0.671287 1.16270i −0.306253 0.951950i \(-0.599075\pi\)
0.977539 0.210752i \(-0.0675914\pi\)
\(720\) 0 0
\(721\) −13.5000 + 23.3827i −0.502766 + 0.870817i
\(722\) −5.19615 3.00000i −0.193381 0.111648i
\(723\) 15.0000i 0.557856i
\(724\) 3.00000 5.19615i 0.111494 0.193113i
\(725\) 0 0
\(726\) −5.00000 8.66025i −0.185567 0.321412i
\(727\) 37.0000i 1.37225i −0.727482 0.686127i \(-0.759309\pi\)
0.727482 0.686127i \(-0.240691\pi\)
\(728\) −2.59808 10.5000i −0.0962911 0.389156i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 0 0
\(732\) −1.73205 1.00000i −0.0640184 0.0369611i
\(733\) 5.00000i 0.184679i 0.995728 + 0.0923396i \(0.0294345\pi\)
−0.995728 + 0.0923396i \(0.970565\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −4.00000 −0.147442
\(737\) 10.3923 + 6.00000i 0.382805 + 0.221013i
\(738\) −5.19615 + 3.00000i −0.191273 + 0.110432i
\(739\) 17.5000 + 30.3109i 0.643748 + 1.11500i 0.984589 + 0.174883i \(0.0559548\pi\)
−0.340841 + 0.940121i \(0.610712\pi\)
\(740\) 0 0
\(741\) 12.5000 + 12.9904i 0.459199 + 0.477214i
\(742\) 39.0000i 1.43174i
\(743\) −20.7846 + 12.0000i −0.762513 + 0.440237i −0.830197 0.557470i \(-0.811772\pi\)
0.0676840 + 0.997707i \(0.478439\pi\)
\(744\) −5.00000 8.66025i −0.183309 0.317500i
\(745\) 0 0
\(746\) 10.0000 0.366126
\(747\) −10.3923 6.00000i −0.380235 0.219529i
\(748\) 0 0
\(749\) −18.0000 −0.657706
\(750\) 0 0
\(751\) −22.0000 38.1051i −0.802791 1.39048i −0.917772 0.397108i \(-0.870014\pi\)
0.114981 0.993368i \(-0.463319\pi\)
\(752\) −7.79423 + 4.50000i −0.284226 + 0.164098i
\(753\) 11.0000i 0.400862i
\(754\) 0 0
\(755\) 0 0
\(756\) −1.50000 2.59808i −0.0545545 0.0944911i
\(757\) 33.7750 19.5000i 1.22757 0.708740i 0.261051 0.965325i \(-0.415931\pi\)
0.966522 + 0.256585i \(0.0825975\pi\)
\(758\) −0.866025 0.500000i −0.0314555 0.0181608i
\(759\) −4.00000 −0.145191
\(760\) 0 0
\(761\) −22.5000 + 38.9711i −0.815624 + 1.41270i 0.0932544 + 0.995642i \(0.470273\pi\)
−0.908879 + 0.417061i \(0.863060\pi\)
\(762\) 5.00000i 0.181131i
\(763\) 25.9808 + 15.0000i 0.940567 + 0.543036i
\(764\) −9.00000 15.5885i −0.325609 0.563971i
\(765\) 0 0
\(766\) −28.0000 −1.01168
\(767\) −3.46410 14.0000i −0.125081 0.505511i
\(768\) 1.00000i 0.0360844i
\(769\) −13.0000 22.5167i −0.468792 0.811972i 0.530572 0.847640i \(-0.321977\pi\)
−0.999364 + 0.0356685i \(0.988644\pi\)
\(770\) 0 0
\(771\) −12.0000 + 20.7846i −0.432169 + 0.748539i
\(772\) 16.0000i 0.575853i
\(773\) −32.0429 18.5000i −1.15250 0.665399i −0.203008 0.979177i \(-0.565072\pi\)
−0.949496 + 0.313778i \(0.898405\pi\)
\(774\) −1.00000 + 1.73205i −0.0359443 + 0.0622573i
\(775\) 0 0
\(776\) −6.00000 + 10.3923i −0.215387 + 0.373062i
\(777\) −2.59808 + 1.50000i −0.0932055 + 0.0538122i
\(778\) 13.8564 8.00000i 0.496776 0.286814i
\(779\) 30.0000 1.07486
\(780\) 0 0
\(781\) −2.00000 −0.0715656
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.73205i 0.0357143 0.0618590i
\(785\) 0 0
\(786\) −7.50000 +